Intraoral imaging system and method based on conoscopic holography

ABSTRACT

A conoscopic holographic system and a method for imaging a scene characterized by a surface having a three-dimensional shape. The system utilizes an optical source, which illuminates the scene with substantially linear distributions of light, and independent register of a plurality of elementary conoscopic holograms in the image plane. Each elementary conoscopic hologram represents the imaging of a single emitting point of the illuminated scene. The optical source is translated relative to the scene to generate a sequence of optical holograms, and a weighted reconstruction of the holograms is performed, in a computer process, at a median plane to devise the three-dimensional shape of the imaged scene.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority from U.S. ProvisionalApplication Ser. No. 61/035,894 filed on Mar. 12, 2008, which isincorporated herein by reference in its entirety.

FIELD OF INVENTION

The present invention relates to non-contacting metrology, and, inparticular, to an apparatus and methods for optical scanning anddigitizing the coordinates of a solid body of complex shape,particularly within a confined space such as a person's mouth.

BACKGROUND ART

Determination of coordinates of points on the surface of an object isoften used for digitizing or imaging of the object, or for variousmanufacturing applications. Some of the known coordinate-measuringprobes are based on conoscopic holography.

The theory of conoscopic holography, a technique implementinginterference of light (which may be spatially incoherent, unpolarized,and/or quasi-monochromatic) emanating from an object for the purposes ofretrieving information about the shape of the object, has been developedby Gabriel Sirat et al. (see, e.g., JOSA A, v. 9, pp. 70-90, 1992, andreferences therein, all incorporated herein by reference). The use ofspatially incoherent light makes it possible to use this technique in alarge variety of environments. Moreover, the spatial resolution ofconoscopic holography in conjunction with photodiode arrays provides fordigital processing of the resulting holograms.

In the basic interference set-up, shown in FIG. 1, an object 1,illuminated with incident light, reflects the light (specularly and/ordiffusely) within a solid angle A. The reflected light r_(i) passesthrough a circular polarizer P1, thereby generating two beams r_(o) andr_(e) with mutually orthogonal polarizations (in phase quadrature), bothof which (and ordinary and extraordinary polarizations, respectively)propagate through a uniaxial crystal 2 having a crystal axis 3, alongapproximately the same geometrical path. These two rays are convertedback to the same polarization mode by a following circular analyzer P2,placed after the crystal 2, and so interfere in the observation (orrecording) plane 4. The circular analyzer P2 also compensates for theinitial quarter-wavelength delay that the ordinary and extraordinarybeams acquire upon propagation through the circular polarizer P1. Theinterference pattern appearing in the observation plane 4 is aconoscopic hologram and represents a superposition of the conoscopicfigures for each point 5 of the object 1. The conoscopic figures foreach point 5 (or for a well-defined set of points) will be referred toherein as “elementary” conoscopic figures. Each elementary conoscopicfigure is formed by interference of light emanating from a particularobject point, and is shaped, in part, according to the position of theemitting object point relative to the fixed recording plane 4. Eachpoint of the object creates its own conoscopic figure, which reveals thetransverse position of the point (based on position with respect to thecenter of the pattern) and distance (based on the density ofinterferometric fringes). Thus, the conoscopic hologram containscomplete information about distances between the emanating object pointsand the recording plane, and, therefore the object's spatialdistribution.

Conoscopic holography, linear or quadratic, may be utilized in manyapplications such as quality control measurements, digitizing, reverseengineering and in-process inspection. Several methods of optical ornumerical reconstruction of conoscopic holograms, allowing for theretrieval of information about the shape of an illuminated object, andthe description of corresponding systems have been reported to-date. Forexample, laser sensors ConoProbe™ and ConoLine™, developed by OpticalMetrology Ltd. (Optimet) of Jerusalem, Israel(http://optimet.com/optimet_company_profile.htm) on the basis ofconoscopic holography, provide contactless three-dimensional measuringof surfaces with submicron resolution. Conoscopic holography is thesubject of various patents, including U.S. Pat. Nos. 4,602,844,4,976,504, 5,081,540, 5,081,541, and 7,375,827, each of which isincorporated herein by reference. In particular, linear conoscopicholography and systems have been disclosed in U.S. Pat. No. 5,953,137,which is also incorporated herein by reference.

In applications such as dental surface profiling for purposes ofreconstruction, orthodontics etc., the relative movement of thepatient's mouth with respect to the sensor and other vibrations duringthe tooth-measurement cycle would impose practical limitations onperformance of the existing systems which are not configured foroperation within a human mouth. Clearly, an automated and robustsolution to the problem of quick digitizing of complex bodies isdesirable. It was also recognized in prior art that performing surfaceand distance measurements on translucent objects such as teeth withconventional techniques such as a three-dimensional automated scanning(see, e.g., WO 2007/071306 to Durbin et al.) results in projected imagesthat are blurred because of the diffusion of light throughout theobject. To overcome such limitation, prior art scanners employopacifying the area of a scene to be imaged by applying an appropriatecoating to it.

SUMMARY OF INVENTION

Embodiments of the invention provide methods for imaging a scenecharacterized by a surface having a three-dimensional shape. Suchmethods have steps of illuminating the scene so as to project onto thesurface of the scene spatially-discontinuous distribution of light thatdefines an instantaneous elementary object, varying with time to producesuccessive elementary objects, and imaging such successive elementaryobjects through an optical coding module to form a sequence ofconoscopic holograms of successive elementary objects. Further, themethods have a step of computing the three-dimensional shape of thesurface based upon the sequence of conoscopic holograms. In someembodiments the imaged scene may be interior to a mouth of a person, andilluminating the scene may include projecting a plurality ofsubstantially linear distributions of light onto the scene. In specificembodiments a plurality of substantially linear distributions of lightmay be represented by equidistantly distributed lines of illumination.

According to other embodiments of the methods of the present invention,a source of illumination may be translated relative to the scene, whichmay be realized by delivering light through a plurality of opticalwaveguides such as optical fibers disposed in a fiber-bundle assembly,or through relay optics optionally including a periscope or a telescope.

In addition, imaging successive elementary objects through the opticalcoding module may include imaging successive elementary objects througha conoscope, and, in some embodiments, evaluation of thethree-dimensional shape of the sample may comprise independentlyanalyzing N elementary conoscopic figures, N being a number of lines inthe plurality of lines of illumination, where each elementary conoscopicfigure represents imaging of a single emitting point on a respectiveline from the plurality of lines of illumination. In specificembodiments of the invention, the evaluation of the three-dimensionalshape of the surface of the scene from the sequence of conoscopicholograms may include evaluating three-dimensional shape of the surfaceof the scene from the sequence of exponential optical conoscopicholograms where a weighted reconstruction of real or exponentialholograms is performed at a median plane.

Furthermore, the method of the invention may include imaging eachsuccessive elementary object without displacement thereof and withrespective different polarization arrangements to form an elementary setof conoscopic holograms, and further comprise processing, in an externalprocessing unit, digital representations of optical conoscopic hologramsfrom the elementary set to remove a bias and a conjugate image.

Other embodiments of the invention provide for a conoscopic holographicsystem comprising an optical source providing a spatially-discontinuousdistribution of light. Here, the conoscopic holographic system mayfurther comprise a periscope projecting the spatially-discontinuousdistribution of light to a scene characterized by a surface, and, inspecific embodiments, project a plurality of substantially lineardistributions of light thereon.

The system of other embodiments may comprise imaging optics configuredto provide independent registration, in an image plane, of N elementaryconoscopic figures. Optionally, each elementary conoscopic figure mayrepresent imaging of a single emitting point on a respectivesubstantially linear distribution of light from the plurality ofsubstantially linear distributions of light, single emitting pointsbeing optical conjugates of photosensitive elements in a detectordisposed in an image plane, the optical conjugates defined by theimaging optics. Some specific embodiments of the system of the inventionmay utilize anamorphic imaging optics.

Yet other embodiments provide methods for determining a distance to anilluminated surface with a linear conoscope, the linear conoscopecharacterized by an image plane and an optical axis, the illuminatedsurface being illuminated with N substantially spatially discontinuousdistributions of light. Such methods entail several computer processes,wherein:

in a first computer process, representing an image signal measured inthe image plane with a detector, as a weighted combination of Nfunctions, each function representing an elementary signal contributedto the image signal by a corresponding single emitting point from therespective discontinuous distributions of light;

in a second computer process, for each of the single emitting points,correlating a weighted test function and the weighted combination togenerate a correlation function, the weighted test function beingweighted with a factor representing a lateral displacement of therespective single emitting point from the optical axis; and

in a third computer process, for each of the single emitting points,determining a longitudinal separation between the image plane and therespective emitting point from a maximum of the correlation function.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing features of the invention will be more readily understoodby reference to the following detailed description taken with theaccompanying drawings, in which:

FIG. 1 depicts the principal features of a prior art conoscopy system;

FIG. 2A is a cutaway view of a conoscopic profilometer in accordancewith an embodiment of the present invention;

FIG. 2B shows the surface irradiation of a tooth in accordance with anembodiment of the present invention;

FIG. 3 depicts an illumination modality in accordance with a furtherembodiment of the present invention;

FIG. 4A illustrates two quadratically-chirped distributions ofirradiance in the observation plane corresponding to two discrete objectpoints;

FIG. 4B is a compound hologram of the signals of FIG. 4A;

FIGS. 5A and 5B show, respectively, compound interferometricdistributions recorded in the observation plane, in accordance withembodiments of the present invention;

FIGS. 6A-6C illustrate the results of reconstruction of the compoundholograms of FIGS. 5A and 5B;

FIGS. 7A and 7B show Wigner-Ville filtered distributions and ashort-term Fourier Transform, respectively, of the distributions of FIG.4A;

FIG. 8 is a flow chart depicting two alternate concepts of aregistration algorithm in accordance with embodiments of the presentinvention;

FIG. 9 schematically depicts the correspondence of a fraction of aconoscopic hologram produced by an instantaneous elementary object, inaccordance with an embodiment of the present invention; and

FIG. 10 is a flowchart depicting a conoscopic measurement withelementary acquisition, full acquisition, and merging processes, inaccordance with an embodiment of the present invention.

DEFINITION OF TERMS

Unless context otherwise requires, in the description of the inventionand accompanying claims the following terms will have meanings asdefined below:

Term Definition Intra-oral three- a system able to characterize or imagea tooth, a group dimensional camera of teeth or a complete jaw using anoptical system introduced in the mouth of a patient Measurement Space ACartesian spatial frame referenced to a predefined fixed point of thesystem, the origin Object a physical object to be measured. Muchinformation exists describing and defining the object such as shape,color, texture, etc. Illumination Module a physical module projecting apredetermined three dimensional light distribution, namely, theillumination light distribution Elementary Pattern an elementary patternis the projection of the illumination light distribution on the x, yplane; in accordance with certain embodiments of the present invention,the elementary pattern may constitute a small number of discrete linesalong the y axis, for example. Illuminated Object an intersection of theillumination light distribution with the object; in practice it mayrepresent stripes on the object, for example. Optical Coding an opticalcoding module is a physical module Module transforming the IlluminatedObject into an optical conoscopic hologram. It is typically built fromcrystals and lenses Optical Conoscopic a two-dimensional optical lightdistribution which Hologram retains information of the three-dimensionalshape of the object. It is a coded version of the three-dimensionaldata. Compound conoscopic a mathematical combination of several opticalhologram conoscopic holograms obtained by multiple values of a physicalparameter. For example, the subtraction of two optical conoscopicholograms in which, in the second one, an additional optical pathdifference of half a wavelength had been added creates a compoundconoscopic hologram without bias. Bipolar and quasi-complex conoscopicholograms have been described in the French patent FR 8817225 DigitalConoscopic a mathematical representation of the optical conoscopicHologram hologram obtained by recording on a detector the lightintensity, digitizing the resulting analog electronic signal and storingthe result in a matrix on a computer or signal processing hardwareDetector Module an optoelectronic apparatus performing the retrieval ofthe digital conoscopic hologram from the optical conoscopic hologramReconstruction a set of mathematical procedures able to retrieve anAlgorithm evaluation the shape of the object - or of the illuminatedobject for a discriminating illumination - from its digital conoscopichologram

DESCRIPTION OF SPECIFIC EMBODIMENTS OF THE INVENTION

Hardware Modules of Embodiments of the Invention

In accordance with certain embodiments of the present invention, aconoscopic profilometer is provided, i.e., a device for determining thedistance from a fiducial reference point to each of a set of points on aspecified surface. Some of the disclosed embodiments are particularlysuited for intraoral dental measurements. Typical component parts of aconoscopic profilometer in accordance with the present invention are nowdescribed with reference to FIG. 2A.

An illumination module 8 of a conoscopic profilometer is an optical oroptomechanical assembly, described in detail below, that generates aspatially-discontinuous light pattern and projects it upon the surfaceof the object to be measured. As used herein and in any appended claims,“spatially-discontinuous” denotes a pattern in which at least twonon-contiguous points are illuminated in a plane transverse to theilluminating beam. The illumination module 8 may include a semiconductorlaser in conjunction with a holographic transmission mask or any othermeans of generating a specified pattern of illumination. In someembodiments, the spatially-discontinuous pattern of light may be in formof a series of substantially linear distributions of light 10 aspresented schematically in FIG. 3. To produce such light distribution,the conoscopic profilometer of the invention preferably utilize ablue-wavelength laser diode (e.g., 405 nm), as compared to 650-685 nmsources conventionally utilized in commercial conoscopic systems. As aresult of working at such shorter wavelength, the system of theinvention provides, among other advantages, higher surface density ofinformation about the measured object (up to 50% more information, sincethe surface resolution increases as ˜1/λ²).

In reference to FIGS. 2A and 3, a schematically shown illuminationmodule 8 of an embodiment of the invention generally includes,therefore, a laser 14 equipped with appropriate imaging optics and anadequate optical or holographic component 16 (array generator, or beamshaper, in FIG. 3) adapted to create a line array pattern 10 in the farfield. It would be understood, however, that different patterns ofillumination such as, for example, a grid of emitting points, can alsoadvantageously be employed in different embodiments of the invention.

The array generator 16, which may also be referred to as a beam shaper,modifies the wavefront of the incident laser beam 18 to a wavefront withspecified irradiance and phase profiles, achieved, in some embodiments,with efficiency exceeding 90%. In embodiments utilizing digital opticsfor the array generator, the single incident laser beam may diffractedby a digital optical element to produce multiple output beamdistribution with specified uniformity and number of beams (or number ofillumination lines per mm in the observation plane with predeterminedlength, width etc). In a specific embodiment, for example, an arraygenerator comprised of a digital optical element can produce apredetermined number of highly uniform equidistantly distributed, sparsestripes or lines of illumination with variation of irradiance, amongequidistant lines, of less than <10% and less than 2% energy remainingin a zeroth order of diffraction.

An objective assembly, in some specific embodiments of the invention mayinclude a periscope in order to allow the system to be convenientlyinserted in the patient mouth. Due to the co-linearity of conoscopicholography, conoscopic sensors are capable of accommodating variousrelay optics such as telescopes or periscopes. As shown in FIGS. 2A and2B, a periscopic component of the objective may be represented by afolding mirror 20, delivering equidistantly distributed stripes or linesof illumination to an intraoral scene 21 to irradiate a surface of atooth. A portion of the surface of the scene, illuminated through theobjective at any moment in time, defines an instantaneous elementaryobject 22.

A translator module (not shown) may be employed with a purpose ofshifting the spatially-discontinuous light distribution relative to theilluminated scene (surface of the object) in order to optically samplethe surface of the object. As a result of a repeated pre-determinedshift of illuminating light pattern with respect to the object, asuccession of elementary objects is formed that is imaged through theoptical coding module to form a sequence of conoscopic holograms ofsuccessive elementary objects, holograms being further analyzed toevaluate three-dimensional shape of the object. Such analysis includes amerging process that involves further repositioning and transforming ofeach of the successive conoscopic holograms into a cloud of points whichare then merged using a merging algorithm. The merging process providesdata about the overall shape of the object, and merging of reconstructedsurfaces utilizing a cloud of points is known in the art.

Realization of embodiments of the translator module may vary. Forexample, while keeping the laser 14 stationary within the profilometer8, the illuminating beam 18 may be displaced with respect to the arraygenerator 16 or the object to be measured with as rotating mirror oroptical wedge or prism. Alternatively, a micropositioning stage can beemployed to translate the laser relative to the scene. Or, the deliveryof laser light to the array generator 16 may be instead realized througha plurality of optical waveguides. Other specific embodiments mayutilize, for example, optical fibers disposed in a fiber-bundleassembly, such as a fiber bundle assembly of N fibers that are litsequentially.

An optical coding module is employed in various of the embodiments ofthe profilometer of the invention, and transforms the light from everypoint of the instantaneous elementary object, into an elementary opticalconoscopic hologram, thereby producing in the observation plane, foreach instantaneous elementary object, a composite conoscopic hologramwhich is an interferometric image representing a superposition ofmultiple elementary conoscopic holograms. A typical optical codingmodule of the invention is generally similar to an apparatus describedin abovementioned patents and schematically illustrated in FIG. 1. Itcomprises an assembly of optical crystals, lenses and polarizers, andwill not be described in further detail.

Each of the composite conoscopic holograms from the sequence ofcomposite holograms, formed in the observation plane by the opticalcoding module as a result of the operation of the translator module, isfurther registered and digitized with a detector module, producingdigital representations of conoscopic holograms. In some of theembodiments, a detector may be a CCD or CMOS matrix with standardresolution (VGA or Megapixel), such as a sufficiently sensitive at theoperational wavelength Kodak KAI-340, for example, providing resolutionof 648*484 pixels and a frame rate of 120 Hz. According to embodimentsof the invention, the detector module is equipped with an anamorphicoptical system configured to provide for independent registration of theconoscopic holograms produced by each elementary-object subset, definedas an optical image of a specific row of pixels in a CCD in objectspace, onto that uniquely corresponding row of pixels. This concept isschematically illustrated in FIG. 9, where each pixel in a pixel-row R1of a detector 24 registers a corresponding fraction of a conoscopichologram produced by only that portion of the instantaneous elementaryobject, formed by illuminating a surface of a scene 26 with the pattern10 of equidistantly-spaced stripes of light, that intersects a linearregion 28 defined as an optical conjugate of the row R1 by an opticalsystem 30 of the embodiment of the invention. In other words, theanamorphic optics of the embodiment of the invention assure that onlyportions r1 through r4 contribute to the conoscopic hologram that willbe viewed by the pixels of the detector row R1, which remains opticallyisolated from any other light emitted by any other portion of theinstantaneous elementary object. Similarly, another row Q1 of pixels inthe CCD 24 receives interfering light only from areas q1 through q4,located at intersections of an optical conjugate 32 of the row Q1 withthe illumination pattern 10. To optimize the registration ofinterferometric information with the detector module, the optical systemof the invention is configured to deliver a corresponding conoscopichologram to each row of the detector.

In addition, the conoscopic profilometer may be equipped with anexternal processing unit 120 (shown in FIG. 2A) that providessignal-processing hardware capable of retrieving the information aboutthe shape of the illuminated surface of the object from the digitalconoscopic holograms or sparse reconstructions, the motion parameters,and the motion-corrected data of the shape of the instantaneouselementary object and data about the overall shape of the objectprovided by the merging algorithm. The external processing unit 120 mayinclude a computer. Embodiments of the conoscopic profilometer of theinvention may also be supplemented with a telemetry unit 130, whichincludes required electronic hardware and software supporting datatransfer and controlling functions of the conoscopic profilometer 8 andthe external processing unit 120.

Examples of Certain Embodiments of the Invention.

As an illustration, now described with reference to the flowchart ofFIG. 10, an intraoral measurement with the use of a conoscopicprofilometer, according to one embodiment of the current invention, maycomprise elementary acquisition, full acquisition, and mergingprocesses.

In an elementary optical acquisition process 140, the intraoral scenemay be, at step 142, illuminated with a pattern consisting, for example,of 16 lines separated from each other by about 1 mm with 480illuminating points per line and forming a single instantaneouselementary object that produces, at step 144, a conoscopic hologramrepresenting a sparse view of the entire object being measured, such asa tooth. The full view of the entire object by each elementaryacquisition, even if carried out with sparse resolution, enablesretrieving parameters of the relative movement of the object inreference to the sensor. Typical dimensions of such an optical hologramin the observation plane may be, for example, 16×17 mm². At step 146,the elementary optical conoscopic hologram is recorded by the detectormodule to produce a digital conoscopic hologram which is a digitalrepresentation of the optical hologram.

According to one embodiment of the invention, the system may furtherperform, at step 148 a, sparse reconstruction of the surface of theilluminated intraoral scene by retrieving from the digital conoscopichologram (with then use of a reconstruction algorithm of the invention)evaluation data representing the shape of the illuminated surface.Alternatively, at step 148 b, the system may keep a digitalrepresentation of the elementary optical conoscopic hologram for furtherprocessing. The data corresponding to the digital conoscopic hologramsor the sparse reconstructions is stored on an appropriate storagemedium, such as a computer memory.

The full optical acquisition is further accomplished at step 150 throughcombining N displaced and interlaced elementary acquisitions byappropriately shifting the illuminating pattern with the translatormodule so as to shift a successive elementary conoscopic hologram in theobservation plane by, for example, an integer number of CCD-pixels withrespect to the previous hologram. In some embodiments, shifting theabovementioned illumination pattern by 75 μm with respect to the imagedscene within a fraction of a second may produce a succession of 12elementary objects in 12 steps over 1 mm distance along the object'ssurface, as well as 12 respectively corresponding elementary opticalconoscopic holograms registered by the detector in the observation planewith a one-pixel shift with respect to one another. In such embodiments,a lateral imaging resolution on the order of 50*100 μm² or better may beachieved.

Finally, in the merging process of step 160, either the successivesparse reconstructions or the successive digital representations aremerged, using the merging process of the invention in the externalprocessing unit, into a single set of data representing evaluation ofthe object shape.

Optionally, a registration algorithm may be used, which allows toevaluate, from each digital conoscopic hologram or from each sparsereconstruction, the relative movement of the object itself that occurredduring the process of measurement of the object's shape, as shown inphantom line at step 162. Here, the movement compensation algorithmrepositions, if necessary, the results of each elementary acquisitionrelative to a global system of coordinates (such as, for example,Cartesian) using the solid movement parameters previously retrieved bythe movement evaluation algorithm.

In some embodiments, a set of several (e.g., two, three or four)elementary optical conoscopic holograms of the same instantaneouselementary object, formed by illumination of the scene with aspatially-discontinuous distribution of light, may be recordedsequentially, in different polarization arrangements, withoutdisplacement of the elementary object by shifting the illuminatingpattern with respect to the scene. Processing the data corresponding toseveral optical conoscopic holograms of the same elementary objectformed with light having different polarization may be required toeliminate parasitic information collected from a coherent continuousbackground (also referred to as bias) and to a conjugate image.Recording of the set of holograms in different polarizations maybeaccomplished, for example, by using, an appropriate light valve switchsuch as the one described in French patent 88-17225, or U.S. Pat. No.5,081,541 to Sirat et al., each of which is incorporated herein in itsentirety. Varying-polarization-based means of elimination of bias andconjugate-image related data have been earlier described in U.S. Pat.No. 5,081,541.

Algorithms of the Embodiments of the Invention

The conoscopic hologram is an optical light distribution which retains,in a two-dimensional format, full information of the three-dimensionalshape of the object. A general exponential conoscopic hologram, asdefined and described by G. Sirat (in JOSA A, v. 9, p. 73, 1992)contains all the three-dimensional information of a convex object withthe same size and resolution. It is, therefore, mathematicallyequivalent to the reconstructed convex object, making the mathematicalproblem solvable.

Due to the presence of noise of physical and digital origin, the dataretrieved from the hologram of the full object suffer from drawbacks andinaccuracies. Algorithms for retrieval and restoration of the data suchas those described by L. M. Mugnier (see “Conoscopic holography: towardthree-dimensional reconstructions of opaque objects”, Appl. Opt., v. 34,pp. 1363-1371, 1995) are known in the art but are not necessarily robustand require iterative solutions.

To simplify the mathematical problem and to make the results moreaccurate and robust, the number of independent variables must bereduced. To that end, the abovementioned commercial systems ConoProbe™and ConoLine™, for example, restrict the measurement of the object to asingle point from each line of data through illuminating the object withlight emanating from a single point (ConoProbe™) or a single line(ConoLine™). However, these systems are quite slow, because they recorda full line for each measurement point or a full frame for a singleline. In particular, in the ConoProbe™, a single point illuminates theentire array; in the ConoLine™, appropriate optics is used in order toseparate, in the second transverse dimension, the contribution fromdifferent points of the line of illumination to separate rows in aCCD-array.

The IntraOral system implementing the current invention is fast enoughand does not compromise the metrological quality of conoscopic sensors.The embodiments of the system utilize a multipoint scheme in whichseveral different points of the same line of illumination from the setof substantially equidistantly distributed lines are recorded at once.The embodiments do not require imaging of a full continuous surface ofthe object, thus increasing the redundancy of information about theobject's surface stored in the compound conoscopic hologram and reducingthe complexity of the required algorithmic solution.

In the IntraOral 3-D Camera of certain embodiments of the presentinvention, for each row of pixels in a CCD, 8 to 16 illuminated objectpoints are projecting light to the same detector pixel row, and thelight on the pixel is a superposition of the contribution of thesepoints. The reconstruction algorithm has to perform first a separationof the contribution of each emitter point to the detector intensity,retaining a measurement metrological capacity equivalent or close tothose of the ConoProbe™ or of the ConoLine™.

This problem represents a theoretically solvable, underconstrainedmathematical problem because a number of emitting points and a number offree parameters is smaller than a number of pixels on the detector. Achosen algorithm must insure complete decorrelation of the signal andnoise terms. The reconstruction algorithm of the invention is based onthe general formalism developed by Sirat, Mugnier and coworkers (see,e.g., the abovementioned reference to Mugnier and reference therein). Incomparison to the general formalism, however, which is applicable toanalyzing continuous two-dimensional elementary object but notsubstantially linear elementary objects, the algorithm used in theembodiments of the invention allowing reconstruction of discrete pointsof substantially one-dimensional objects.

The algorithm is applied separately to data obtained from each line ofthe digital conoscopic hologram, referred to as a signal, performs aweighted reconstruction of the exponential hologram at a median plane,situated at the middle of the measuring range. and processes a datumobtained from each emitting point of the instantaneous elementary objectseparately. At wavelengths where the material of the scene is at leastpartly translucent (i.e., permitting light to penetrate through thesurface but diffusing it), the algorithms of the invention filters outthe data associated with object reflections originating beyond thesurface of the scene based on, among other factors, the known propertiesof the material.

The mathematical problem, therefore, is to retrieve longitudinalpositions and energy in a conoscopic hologram from a small number ofpoints the lateral positions of which are known. For the case of aone-dimensional exponential hologram, the one-dimensional distributionof intensity in the image plane S(x) is

$\begin{matrix}{{S(x)} = {\sum\limits_{i = 1}^{N}{A_{i}{\exp\left\lbrack {{{j\alpha}_{i}\left( {x - x_{i}} \right)}^{2} + {\varphi_{i}\left( \alpha_{i} \right)}} \right\rbrack}}}} & (1)\end{matrix}$

where S(x) is the signal intensity measured at each frame; A_(i) andα_(i) are the unknown parameters defined below, α_(i) being a functionof longitudinal position of each point characterized by a lateralposition x_(i), and x_(i) and φ_(i)(x) are parameters measured duringand known from the system calibration.

Embodiments of the current invention adapt three strategies to solve theabovementioned mathematical problem, among which are a modifiedSirat-Mugnier algorithm (wave-reconstruction formalism), Time Frequencyalgorithms, and Maximum Likelihood Expectation approach.

(1) Reconstruction Algorithm: Wave Propagation Formalism

The reconstruction algorithm is applied separately to each line of thedigital conoscopic hologram, referred to as a signal. The analysis ofeach line is performed separately, and, as a result, the mathematicaltwo-dimensional problem is transformed to N sets of one-dimensionaldata, with N being the number of lines in the hologram, thus greatlyreducing the number of variables and removing the continuity uncertaintyof a general unknown pattern.

The light intensity reflected by each point of the elementary object,which is defined by illuminating the surface of the scene with aplurality of equidistantly distributed stripes or lines of light, thepoints having the same position on the respective line, produce apattern on one column of the matrix expressed by:

$\begin{matrix}{{I(x)} = {\sum\limits_{i}{A_{i}\left\lbrack {\cos\left( {\alpha_{i}\left( {x - x_{i}} \right)} \right)} \right\rbrack}^{2}}} & (2)\end{matrix}$

Or, more generally, through an exponential function as described in Eq.(1) above, where α_(i) is a function of z, z being the longitudinaldistance between the observation plane and the respective emittingpoint, A_(i) is the irradiance produced by the emitting point, and X_(i)is the point's lateral position with respect to the geometrical axis ofthe profilometer.

In embodiments with a telecentrically designed optical coding module,x_(i) is constant; for non-telecentric design x_(i) varies with distancez according to a known function. The compound optical hologram signalwould correspond to a discretized signal represented by a sum(superposition) of N (where, in some embodiments, N=16)quadratically-chirped irradiance signals associated with opticalconoscopic holograms formed by discrete emitting points. A quadraticchirp, corresponding to linear modulation of spatial frequency of thecorresponding irradiance distribution in the observation plane, isproportional to z, while position of the center of the interferometricpattern is descriptive of a position of the corresponding emittingobject point in xy-plane. As an example, FIG. 4A illustrates twoquadratically-chirped distributions of irradiance in the observationplane, I1 and I2, respectively corresponding to two discrete emittingobject points, E1 and E2 (not shown), that are shifted laterally withrespect to the geometrical axis of the quadratic conoscope of theinvention. As would be understood by one skilled in the art, thedistances between the two points and the observation plane are different(i.e., z₁≠z₂), as follows from the different numbers of fringes incorresponding interferometric distributions. FIG. 4B represents acompound hologram I12 corresponding to distributions I1 and I2 of FIG.4A and shows a superposition of the two signals in the observationplane. FIGS. 5A and 5B show, respectively, compound interferometricdistributions (optical conoscopic holograms) I34 and I56, recorded inthe observation plane and respectively formed by light emanating fromrespectively corresponding pairs of object points, (E3, E4) and (E5,E6), not shown. The emitting points in either pair are shifted laterallyand symmetrically from the geometrical axis of the conoscope by 24pixels. However, while E3 and E4 are equidistant from the observationplane (individual distributions I3 and I4, not shown, contain 64 fringeseach), E5 and E6 are located at different distances (individualdistributions I5 and I6, not shown, contain 60 and 64 fringes,respectively). As shown in each of FIGS. 5A and 5B, traces a representreal parts of the respective distributions, while traces b correspond tothe imaginary parts.

The algorithm reconstructs the two holograms in a median plane, in whichthe contributions of the two signals are separated spatially, andprocesses separately each one of the signals separately. Signalprocessing is performed by removing a real part of the holographic dataand applying a Wiener-filter to the imaginary part. FIGS. 6(A. B, C)illustrate the results of reconstruction of the compound holograms ofFIGS. 5A and 5B, respectively. In FIGS. 6A and 6B, signals 60, 62 and64, 66 associated with corresponding object points are well separatedand the spurious interference is optimized in the central portions ofthe reconstruction patterns (although they are still present in theperipheral regions). FIG. 6C, which is a zoom-in of FIG. 6B, shows thedisappearance of the spurious interference in the region of the signals.

In a modified Sirat-Mugnier reconstruction algorithm, S(x) of Eq. (1) iscorrelated with m weighted exponential functionsT _(mn)(x)=(x−x _(n))exp[jα _(m)(x−x _(n))²+φ_(mn)]  (3)

and, for each emitting point n, the correlating figures U_(mn)U _(mn)=∫(x−x _(n))T _(mn)(x)S(x)  (4)

are analyzed, where (x−x_(n)) is a lateral displacement of emittingpoint n from the optical axis of the conoscope. The maximal value U_(mn)represents the best correlation, and, therefore, corresponds to theoptimally determined longitudinal distance associated with parameter m.To increase precision of determination of the longitudinal distance,additional parabolic fitting is performed, corrected by interferenceeffects. In doing so, to U_(mn) by intensity in the n−1 and n+1 pointsis appropriately considered. This embodiment of the algorithms of theinvention differs from the original Sirat-Mugnier two-dimensionalalgorithm, described in the above-referenced article by Mugnier, by amultiplier (x−x_(n)). The need for the additional multiplier would beunderstood from the energy distribution in each cycle. In 2D, the energypresent in a cycle is equal to the energy present in another cycle dueto the equation of the surface of a ring. To reach the equivalentcondition in 1D we need to add a linear weighting function.

(2) Reconstruction Algorithm: Time-Frequency Formalism

In the Time-Frequency algorithm, first a general Time Frequencyalgorithm is applied to data; additionally, the unknowns A_(i) and α_(i)are retrieved parametrically from the 2D Time-Frequency surface usingknown parameters x_(i) and φ_(i)(x).

Several time-frequency algorithms for signal processing are known in theart, such as, for example, Wigner-Ville distribution or the short-termFourier Transform. FIGS. 7(A, B) respectively represent atwo-dimensional and three-dimensional views of the Wigner-Villetransform of the distributions I1 and I2 of FIG. 4A, which readilydemonstrate two symmetric line-patterns.

(3) Reconstruction Algorithm: Maximum Likelihood Approach

Finally, in determining A_(i) and α_(i) through the Maximum LikelihoodExpectation approach, the results of one of the previous algorithms canbe used as a starting point to minimize the search space for parametersA_(i) and α_(i).

(4) Registration Algorithm (Repositioning and Merging)

The registration algorithm of preferred embodiments of the currentinvention is based on the continuous measurement of the relativeposition of the object with respect to the instrument. The algorithm mayrely only on the recorded data, without recourse to any additionalexternal references however the use of a separate mechanism forestablishing relative displacement is also within the scope of thepresent invention.

The registration algorithm utilizes a linear differential from frame toframe. In a examplary profiling of the scene at a rate of about 10 mmper 1 sec, the scanning speed will be approximately constant (withinabout 25%, below 20 μm volumetric change from frame to frame). The viewof the full object, in each elementary acquisition provides a largerbasis for the calculation of the relative movements of the objectitself. In one implementation, the global position parameters can bedirectly retrieved from the hologram differences. FIG. 8 illustrates twoalternative concepts of the registration algorithm in accordance withembodiments of the present invention. Algorithms for merging thereconstructed surfaces utilizing a cloud of points are known in the art.

Measuring Objects Made of Translucent Materials

In the context of this disclosure, as discussed above and unlessrequired otherwise, optically measuring a three-dimensional objectimplies measuring the spatial position of a light distribution, createdby an adequate source of illumination, at the physical object. Assumingthat object is opaque, the light-reflecting surface of is the outerphysical surface of the object. This assumption is valid for mostobjects, but fails for those that are semi-transparent or translucentobjects. The light penetrates the physical surface boundary of atranslucent object down to the depth that defines what is known in theart as “skin layer.” Consequently, the reflected light emerges not onlyfrom the surface points but also from a spatial region positioned belowthe surface. In other words, each illuminated point at the surface ofthe translucent object there is a group of points in the depth of theobject that are also illuminated, thus effective broadening the size ofthe light distribution serving as an instantaneous elementary object forembodiments of the system of the invention. For translucent materialscharacterized by some absorbance figure, the intensity of lightdistribution within the object is depth dependent, and an averagepenetration depth can be used to characterize such dependency.

It would be understood that the conoscopic systems, where the strengthof the reflected by the object signal is proportional to the cosine ofthe longitudinal position of the illuminated spot of the object, areideally fitted to work with translucent materials. In such systems, thepenetration-depth-dependent light distribution resembles the surfacelight distribution of Eq. (2) up to a second order of magnitude O(z₀ ²)in a variable z₀ related to a weighted average of the longitudinalposition z:

$\begin{matrix}{{\int_{z_{0} - {\Delta\; z}}^{z_{0} + {\Delta\; z}}{{I(z)}{\cos\left( {\alpha\; z} \right)}{\mathbb{d}z}}} = {{{\cos\left( {\alpha\; z_{0}} \right)}{\int_{z_{0} - {\Delta\; z}}^{z_{0} + {\Delta\; z}}{{I(z)}{\mathbb{d}z}}}} + {O\left( z_{0}^{2} \right)}}} & (5)\end{matrix}$

It is understood that operation of the embodiments of the inventionrequires programmable computer instructions, configuration, and supportembodying all or part of the functionality previously described withrespect to the invention and loaded onto a computer. Those skilled inthe art should appreciate that such computer instructions and supportcan be written in a number of programming languages for use with manycomputer architectures or operating systems. For example, someembodiments may be implemented as entirely software (e.g., a computerprogram product) in a procedural programming language (e.g., “C”) or anobject oriented programming language (e.g., “C++”). Furthermore, suchinstructions may be stored in any memory device, such as semiconductor,magnetic, optical or other memory devices, and may be either transmittedto the computer using any communications technology (such as optical,infrared, microwave, or other transmission technologies) or embedded init in a form of a programmable hardware chip with a computer programproduct fixed in it. It is expected that such a computer program productmay be distributed as a removable storage medium with accompanyingprinted or electronic documentation (e.g., shrink wrapped software),preloaded on the computer (e.g., on a computer ROM or fixed disk), ordistributed from a server or electronic bulletin board over the network(e.g., the Internet or World Wide Web). Of course, some embodiments ofthe invention may be implemented as a combination of both software andhardware. Still other alternative embodiments of the invention can beimplemented as pre-programmed entirely hardware elements.

The embodiments of the invention heretofore described are intended to bemerely exemplary and numerous variations and modifications will beapparent to those skilled in the art, including various combinations offour different methods that have been described. All such variations andmodifications are intended to be within the scope of the presentinvention as defined in any appended claims.

What is claimed is:
 1. A method for imaging a scene characterized by asurface having a three-dimensional shape, the method comprising: a.illuminating the scene so as project onto the surface of the scene aplurality of light stripes from a source of illumination, the pluralityof light stripes defining an instantaneous elementary object, theinstantaneous elementary object varying with time to produce asuccession of elementary objects; b. imaging the succession ofelementary objects through an optical coding module to form a sequenceof conoscopic holograms, each conoscopic hologram respectivelycorresponding to an elementary object from the succession of theelementary objects; and c. computing the three-dimensional shape of thesurface based upon the sequence of conoscopic holograms.
 2. A methodaccording to claim 1, wherein the scene is interior to a mouth of aperson.
 3. A method according to claim 1, wherein the surface includestranslucent material.
 4. A method according to claim 1, whereinilluminating the scene includes varying a relative position between thesource of illumination and the scene.
 5. A method according to claim 4,wherein varying the relative position includes translating a source ofillumination relative to the scene.
 6. A method according to claim 1,wherein illuminating the scene further comprises delivering light from asource of illumination through a plurality of optical waveguides.
 7. Amethod according to claim 6, wherein the optical waveguides includeoptical fibers disposed in a fiber-bundle assembly.
 8. A methodaccording to claim 1, wherein illuminating the scene includesilluminating the scene through relay optics.
 9. A method according toclaim 8, wherein illuminating the scene includes illuminating the scenethrough a periscope.
 10. A method according to claim 8, whereinilluminating the scene includes illuminating the scene through atelescope.
 11. A method according to claim 1, wherein imaging thesuccessive elementary objects through the optical coding module includesimaging the successive elementary objects through a conoscope.
 12. Amethod according to claim 1, wherein evaluating the three-dimensionalshape of the surface of the scene further comprises independentlyanalyzing N elementary conoscopic figures, N being a number of lines inthe plurality of lines of illumination, each elementary conoscopicfigure representing imaging of a single emitting point on a respectiveline from the plurality of lines of illumination.
 13. A method accordingto claim 1, wherein evaluating the three-dimensional shape of thesurface of the scene from the sequence of conoscopic holograms includesevaluating three-dimensional shape of the surface of the scene from thesequence of exponential optical conoscopic holograms.
 14. A methodaccording to claim 13, further comprising a weighted reconstruction ofexponential holograms at a median plane.
 15. A method according to claim1, wherein imaging the successive elementary objects through the opticalcoding module to form the sequence of optical conoscopic holograms ofthe succession of elementary objects includes imaging a successiveelementary object without displacement thereof and with respectivedifferent polarization arrangements to form an elementary set ofconoscopic holograms.
 16. A method according to claim 15, furthercomprising processing, in an external processing unit, digitalrepresentations of optical conoscopic holograms from the elementary setto remove a bias and a conjugate image.
 17. A conoscopic holographicsystem comprising: an optical source; an array generator for providing aplurality of light stripes; a detector array for registering a pluralityof conographic holograms based on the light stripes; and a processor formeasuring a distance from a specified point on a surface of a body to afiducial reference position based on the plurality of conographicholograms and for generating a signal representing the distance.
 18. Aconoscopic holographic system according to claim 17, further comprisinga periscope projecting the plurality of stripes of light onto a scenecharacterized by a surface.
 19. A conoscopic holographic systemaccording to claim 17, further comprising imaging optics configured toprovide independent registration, in an image plane, of N elementaryconoscopic figures.
 20. A conoscopic holographic system according toclaim 19, wherein each elementary conoscopic figure represents imagingof a single emitting point on a respective substantially lineardistribution of light from the plurality of substantially lineardistributions of light, single emitting points being optical conjugatesof photosensitive elements in a detector disposed in an image plane, theoptical conjugates defined by the imaging optics.
 21. A conoscopicholographic system according to claim 19, wherein the imaging optics areanamorphic.
 22. A method for determining a distance to an illuminatedsurface with a linear conoscope, the linear conoscope characterized byan image plane and an optical axis, the illuminated surface beingilluminated with N substantially linear distributions of light, themethod comprising: in a first computer process, representing an imageirradiance measured in the image plane with a detector as a weightedcombination of N functions, each function representing an elementarysignal contributed to the image irradiance by a corresponding singleemitting point from a respective linear distribution of light; in asecond computer process, for each of the single emitting points,correlating a weighted test function and the weighted combination togenerate a correlation function, the weighted test function beingweighted with a factor representing a lateral displacement of therespective single emitting point from the optical axis; and in a thirdcomputer process, for each of the single emitting points, determining alongitudinal separation between the image plane and a respectiveemitting point from a maximum of the correlation function.